As machine-to-machine (M2M for short) communication applications increase rapidly, market demands and scale of the machine-to-machine communication applications have met explosive growth in recent years. Because the M2M applications have a requirement for low costs, a crystal oscillator of user equipment is relatively rough, and consequently, a system carrier frequency offset caused by the crystal oscillator is relatively high. The M2M applications may also need to support an application scenario with mobility of user equipment. In a scenario with high mobility, a Doppler frequency shift is relatively significant, which greatly affects an existing carrier frequency offset estimation method. In addition, because the M2M applications have a requirement for low power consumption, a channel transmission bandwidth is low, and a signal transmission power is also low. Therefore, reducing uplink and downlink channel transmission bandwidths is a relatively effective technical method for reducing power consumption. However, in a narrowband system, because a system symbol rate is low, an estimation range of the existing carrier frequency offset estimation method is small, and when the estimation range of the method is exceeded, a frequency offset estimation value is inaccurate.